Any arbitrary system can have at least two states. The system can be, for example, an apparatus, a human body, or a financial entity. Typically, the system either functions correctly (normal state) or has a malfunction (error state). There may be several normal and/or error states. A good example is the healthiness of a human: he or she can be healthy (normal state) or have a disease (error state), in which case the number of the error states is very large. The state of the system defines in which normal or error state the system is and how much the state of the system differs from a reference state specified beforehand. For example, in medical applications the state of the system defines the disease a patient has and how far the disease has advanced, as compared with the normal, healthy state, or the state of the system defines the malfunction of an apparatus and how severe the malfunction is.
Computerized methods are needed in the above-mentioned analyses of the state of the system to efficiently utilize multidimensional data and to find complex correlations in the data. Each dimension relates to an aspect of the particular system that is being measured and from which measurement values are gathered. Typically, the computerized methods give only a classification as an output. However, in many applications the computerized methods cannot make the final decision because of possible erroneous decisions, but a human user has to make the final decision. The computerized methods should be regarded as an extra resource for users, which supports the decision making but does not try to replace the users and their knowledge and experience.
The computerized methods should provide the user with an accurate, reliable, continuous index on the state of the system, not just a binary classification result (normal or failure). For example, in computer-assisted diagnosis, the computerized method has to give to a physician information on how probable it is that a patient has a disease, so that this information would be helpful for the physician in the decision-making.
In the conventional computerized methods, the classification is carried out based on only one measurement and the detection is carried out using one error state and one normal state only. One measurement may give decent classification results when there is only one possible error state. However, in practice, the possible error state is not known, but the data of the system has to be compared with all existing error states. However, measurement values are probably overlapping when many error states are studied simultaneously, and the classification is inaccurate when only one measurement is used. On the other hand, if the possible error state of the system is detected, it would be useful to know how severe the error state is.